Todd M. answered • 10/17/19

Knowledgeable and patient Tutor for Finance and the Series 65 Exam

Rebecca,

You're very close to your answer. You're correct, one standard deviation in each direction accounts for 68% of the scores. Two standard deviations in each direction will account for 95% of the results (range of 412 to 592) and three will account for 99.999% of the results, or effectively 100% (range of 367 to 637).

So the question is really asking for the odds of going beyond two standard deviations, but only on one side of the distribution curve. In total going from 2 standard deviations to three covers the distance between 95% and 100%, or 5%. Since we're only looking at one side of the curve, there is 2.5% chance the score will be above 592.